Antônio Mesquita

The authors are happy to offer here the complete version of the annotated English translation of the ancient Greek and Latin Lives of Aristotle, which is part of the new complete works of Aristotle organised by C.D.C. Reeve for Hackett Publishing. The translation that will be included in this collection is an abridged and simplified version of the one we have prepared and present here, particularly with regard to the notes. We are grateful to the president of Hackett Publishing Company, Deborah Wilkes, for her unreserved authorisation for this publication, and to the director of Archai, Gabiele Corneli, for his interest in welcoming it into the pages of this journal. This work is financed by national funds through FCT - Fundação para a Ciência e a Tecnologia, I.P., within the scope of the project for the Annotated Translation of the Complete Works of Aristotle (6th Phase) (PTDC/FER-FIL/0305/2021).

This paper aims at clarifying the procedure of proofs by _reductio ad impossibile_ in Aristotle’s _Prior Analytics_, especially elucidating what can be taken as impossibility in such proofs. Traditional interpretation has it that the impossibility in Aristotle’s _reductio_ proofs must be a contradiction. I argue for an alternative interpretation according to which both contrarieties and contradictions are suitable as the impossibility required by the proofs in question. I also present a definition of proof by _reductio ad impossibile_ in accordance with the alternative interpretation.

This article discusses the definition of paraconsistency understood as the property of a consequence relation that does not trivialize inconsistent theories. Some logicians have argued that standard paraconsistency, the requirement of a non-explosive consequence relation, is insufficient for that purpose. In this article, we have a twofold goal. First, we offer an exposition of some attempts to strengthen standard paraconsistency in the literature. After discussing the shortcomings of those attempts, we examine the concepts of triviality in relation to which those concepts of paraconsistency are defined. Then, as our second goal, we propose an alternative definition of paraconsistency that aims to avoid the trivialization of inconsistent theories in a stricter sense.